Peter,
You asked: ...(copied to mine)
«I'm interested in why & how the motions of larger bodies further away are assumed to be a different case to smaller closer bodies».
«Surely there aren't two different 'types' of gravity?».
Answer: «there are no two types of gravity».
There is the only remote mechanism in the Universe for forming the force of interaction between the elements of matter, which is realized as a result of the interaction of the de Broglie toroidal gravitational waves at the common frequencies of the parametric resonance (entanglement effect).
This quantum mechanism of gravity is shown in a photo of phenomena observed in outer space (essay 2017) https://fqxi.org/community/forum/topic/2806.
On the photo https://drive.google.com/file/d/0B1MvF-AefpMmNWJ2MGJkRmJvR00/ two interacting large bodies are shown which, using a multitude of toroidal gravitational waves, move small elements of Saturn's rings (their moving is an indicator of the action of force between bodies) https://saturn.jpl.nasa.gov/resources/4755/?category=images. It should be noted that there are no toroidal gravitational waves directly connecting the bodys. Toroidal gravitational waves interact with each other only at Lagrange points.
Similarly, with the help of toroidal gravitational waves, the Earth and the Moon interact, and the ocean tides are indicators of their interaction
https://drive.google.com/file/d/1hzn3q0vZVToxOMVFkwGsRlOxnNeb9OiY/.
Orbital toroidal gravitational waves are formed due to parametric resonance in the medium of the physical vacuum (these are soliton waves), which minimize the force of interaction between bodies in a very rigid superfluid medium of the physical vacuum.
Ie, any force leads to the formation of toroidal gravitational waves aimed at minimizing the force, including minimizing the inertia force. Therefore the force of attraction of the Moon to the Earth is minimized, and the law of gravitation of Newton is unfair for both stars in galaxies and for orbital bodies.
Those. The moon is in orbit in the potential well of gravitational fundamental interaction and is not attracted to the Earth. All fundamental interactions have a potential stability pit as a strong interaction.
For example, no one uses the law of gravitation of Newton to calculate the ephemeris of planets and satellites. It is impossible to explain complex trajectories of the orbital motion of bodies without quantum reformation of toroidal gravitational waves. On a photo of rings of Saturn https://saturn.jpl.nasa.gov/system/resources/detail_files/5512_IMG004512.jpg
depicts the principle of the formation of a complex trajectory of the orbital motion of the small bodies of the rings of Saturn under the action of toroidal gravitational waves of two gravitationally interacting satellites of Saturn. And here is showed, complicated moving of the Pioneers https://drive.google.com/file/d/0B1MvF-AefpMmVXJfWjF1VF9JaVU/ .
However, the mechanism of minimizing the force with the help of toroidal gravitational waves is not ideal. No ideality is caused by the absorption coefficient in the medium of the physical vacuum (the Hubble parameter).
In order that the Moon does not fall from the orbit, due to the imperfection of the mechanism of minimizing the force of its attraction to the Earth, on the Moon constantly acts the force that pushes the Moon in orbital toroidal gravitational wave with an equivalent speed of 1 km/s (the first cosmic velocity of the Moon). Therefore, on the surface of the Moon, a gravitational potential is formed equal to the square of the equivalent speed of 1 km/s.
A constant force is also acting on the Earth, it pushes forward it on orbit around the Sun by a stream of physical vacuum in a toroidal gravitational wave, with an equivalent velocity of 8 km/s (this was discovered by Michelson and Morley). Accordingly, a gravitational potential equal to the square of the equivalent velocity of 8 km/s (the first cosmic velocity of the Earth) is formed on the Earth's surface.
For example, it was found that the Sun moves relative to the propagation medium of microwave radiation at a speed of 369 km/s. To minimize the resistance force in a rigid environment of physical vacuum, the Sun forms a huge gravisphere, several light-years in size. The force of the deceleration of the sun in the medium of the physical vacuum is determined by the Hubble parameter, as is the anomalous inhibition of the Pioneers and the red shift of the photons. The entire energy of the braking of the solar system is concentrated in the Sun according to the principle of the action of the heat pump. Through the force of deceleration of the Sun, its radiation power is easily calculated.
Thus, one of the most fundamental parameters in the universe is the energy dissipation coefficient (Hubble parameter) in the medium of the physical vacuum, which determines all the parametric processes in the universe. The stars in the Universe are shining, due to the dissipation of photon energy in the medium of the physical vacuum.
You also asked:
«i.e. there's no explicit proof of the 'curved space-time' hypothesis in the LIGO finding. Is that fair?»
Instead of curvature of space-time, there is a derivative of spatial coordinates in time. Equivalent of "'curved space-time" is the variable speed of propagation of gravitational interaction.
For example, on the surface of the Earth, the velocity of propagation of the gravitational interaction is 8 km/s less than at the periphery of the Earth's gravisphere. Therefore, the elements (gravitons) of toroidal gravitational waves (similarly to the coronal loops on the Sun) are accelerated in bodies, when exiting the Earth (or are decelerated in bodies, at the entrance to the Earth). Thus, the reactive force of attraction of bodies is formed.
In the Earth's magnetosphere often occur conversion powerful toroidal gravitational waves. In this case, there are intense https://drive.google.com/open?id=0B1MvF-AefpMmQnJaUXdOTEo4NW8 bursts of electromagnetic radiation over a wide frequency range and recorded the characteristic signals of gravitational waves LIGO project, that unreasonably taken as the signals from the "binary pulsars".
Vladimir Fedorov
https://fqxi.org/community/forum/topic/3080